WhittakerM
The Whittaker M function
WhittakerW
The Whittaker W function
Calling Sequence
Parameters
Description
Examples
References
WhittakerM(mu, nu, z)
WhittakerW(mu, nu, z)
mu
-
algebraic expression
nu
z
The Whittaker functions WhittakerM(mu, nu, z) and WhittakerW(mu, nu, z) solve the differential equation
y''+−14+μz+14−ν2z2y=0
They can be defined in terms of the hypergeometric and Kummer functions as follows:
WhittakerMμ,ν,z=ⅇ−12zz12+νhypergeom12+ν−μ,1+2ν,z
WhittakerWμ,ν,z=ⅇ−12zz12+νKummerU12+ν−μ,1+2ν,z
WhittakerM1,2,0.5
0.1606687379
diffWhittakerWμ,ν,z,z
12−μzWhittakerWμ,ν,z−WhittakerWμ+1,ν,zz
seriesWhittakerM2,3,x,x
x72−2x927+23x112448+Ox132
seriesWhittakerW−12,−13,x,x
33Γ232x162π−π3x56Γ232+93Γ232x764π−3π3x11610Γ232+93Γ232x13616π−3π3x17640Γ232+273Γ232x196224π−9π3x236880Γ232+273Γ232x2561792π−9π3x2967040Γ232+813Γ232x31646592π−27π3x356239360Γ232+Ox376
simplifyWhittakerWμ+73,ν,x
−μ−16−νν+μ−16x−2μ−83WhittakerWμ−23,ν,x+5μ2+−4x+253μ+x2−ν2−10x3+8936WhittakerWμ+13,ν,x
Abramowitz, M., and Stegun I. Handbook of Mathematical Functions. New York: Dover Publications.
Luke, Y. The Special Functions and Their Approximations. Vol 1. Academic Press, 1969.
See Also
hypergeom
inifcns
KummerU
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